How do I start a cloth simulation after an animation?
The simulations in Blender usually all come with an option for caching, and the place to cache the cloth simulation also serves as a control from when to when the simulation will be taking place.



Here a little visual demonstration:


So to speak of the most simple solution, all you have to do is to set up the simulation and limit the start and maybe the end (means the cloth would not continue falling or folding and just stay stiff in the last calculated form) of each cloth object simulation.

Happy Blending